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Incremental N-mode SVD for large-scale multilinear generative models.

Minsik Lee, Chong-Ho Choi

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
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    This summary is machine-generated.

    This study introduces an improved incremental N-mode singular value decomposition (SVD) for handling large-scale tensor data. The method offers full factorization results for generative models and efficient updates with new data.

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    Area of Science:

    • Machine Learning
    • Data Science
    • Signal Processing

    Background:

    • Tensor decomposition, particularly N-mode singular value decomposition (SVD), is vital for analyzing high-order data in machine learning and image processing.
    • Direct N-mode SVD faces memory limitations with high-dimensional data.
    • Existing incremental methods for N-mode SVD offer incomplete factorization, limiting their application.

    Purpose of the Study:

    • To present a complete derivation of incremental N-mode SVD.
    • To enable the application of incremental N-mode SVD in generative models.
    • To reduce computational costs and facilitate efficient updates with new data.

    Main Methods:

    • Developed a complete derivation for incremental N-mode SVD.
    • Introduced a calculation reordering technique to reduce computational complexity.
    • Demonstrated the method's capability for updating existing N-mode SVD results.

    Main Results:

    • The proposed incremental N-mode SVD provides full factorization results, suitable for generative models.
    • A significant reduction in computational cost was achieved through calculation reordering.
    • The method effectively approximates N-mode SVD for experimental data and efficiently updates multilinear models.

    Conclusions:

    • The enhanced incremental N-mode SVD overcomes memory limitations for large-scale tensor decomposition.
    • The method supports generative modeling and provides efficient updates for dynamic datasets.
    • This approach offers a computationally efficient and comprehensive solution for N-mode SVD.